Details

analyze2.0s

Algorithm

Search

True	Other	False	Iter
0%	99.6%	0.4%	0
0%	99.6%	0.4%	1
0%	99.6%	0.4%	2
0%	99.6%	0.4%	3
0%	99.6%	0.4%	4
0%	99.6%	0.4%	5
0%	99.6%	0.4%	6
0%	99.6%	0.4%	7
0%	99.6%	0.4%	8
0%	99.6%	0.4%	9
0%	99.6%	0.4%	10
0%	99.6%	0.4%	11
0%	99.6%	0.4%	12
0%	99.6%	0.4%	13
0%	99.6%	0.4%	14

sample40.0ms

Algorithm

intervals

Results

22.0ms	256×	body	128	valid
1.0ms	11×	body	128	invalid

simplify208.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (201.0ms)

Iter	Nodes	Cost
0	4834	49
1	4834	49

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 29.9b

Counts

2 → 1

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x y) z) y) 471841060772561/17179869184) y)
0.1b	(.f64 (+.f64 (.f64 (+.f64 y a) y) b) y)
0.1b	(.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y)
29.0b	(/.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184) y) 7925469156333415/34359738368) y) t) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`pow1_binary64`
9×	`associate-r_binary64` `associate-l_binary64` `times-frac_binary64`
6×	`associate-*l/_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l_binary64` `*-commutative_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 91

Calls

4 calls:

12.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x y) z) y) 471841060772561/17179869184) y)
11.0ms	(.f64 (+.f64 (.f64 (+.f64 y a) y) b) y)
14.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y)
32.0ms	(/.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184) y) 7925469156333415/34359738368) y) t) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

series1.0s

Counts

4 → 12

Calls

4 calls:

109.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x y) z) y) 471841060772561/17179869184) y)
55.0ms	(.f64 (+.f64 (.f64 (+.f64 y a) y) b) y)
118.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y)
762.0ms	(/.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184) y) 7925469156333415/34359738368) y) t) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

simplify80.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4969	3432
1	4969	3432

prune207.0ms

Filtered

88 candidates to 103 candidates (-17.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	90	13	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	13	104

Merged error: 28.4b

Counts

104 → 13

localize36.0ms

Local error

Found 4 expressions with local error:

18.3b	(cbrt.f64 (+.f64 (*.f64 (+.f64 y a) y) b))
18.3b	(cbrt.f64 (+.f64 (*.f64 (+.f64 y a) y) b))
18.3b	(cbrt.f64 (+.f64 (*.f64 y (+.f64 y a)) b))
29.0b	(/.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184) y) 7925469156333415/34359738368) y) t) (+.f64 (.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 (+.f64 y a) y) b)) (cbrt.f64 (+.f64 (.f64 (+.f64 y a) y) b))) (.f64 y (cbrt.f64 (+.f64 (*.f64 y (+.f64 y a)) b)))) c) y) i))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`times-frac_binary64` `cbrt-prod_binary64`
6×	`cbrt-div_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `pow1_binary64`
3×	`associate-/r_binary64` `pow1/3_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 70

Calls

4 calls:

7.0ms	(cbrt.f64 (+.f64 (*.f64 (+.f64 y a) y) b))
7.0ms	(cbrt.f64 (+.f64 (*.f64 (+.f64 y a) y) b))
7.0ms	(cbrt.f64 (+.f64 (*.f64 y (+.f64 y a)) b))
56.0ms	(/.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184) y) 7925469156333415/34359738368) y) t) (+.f64 (.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 (+.f64 y a) y) b)) (cbrt.f64 (+.f64 (.f64 (+.f64 y a) y) b))) (.f64 y (cbrt.f64 (+.f64 (*.f64 y (+.f64 y a)) b)))) c) y) i))

series1.4s

Counts

4 → 12

Calls

4 calls:

199.0ms	(cbrt.f64 (+.f64 (*.f64 (+.f64 y a) y) b))
199.0ms	(cbrt.f64 (+.f64 (*.f64 (+.f64 y a) y) b))
200.0ms	(cbrt.f64 (+.f64 (*.f64 y (+.f64 y a)) b))
780.0ms	(/.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184) y) 7925469156333415/34359738368) y) t) (+.f64 (.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 (+.f64 y a) y) b)) (cbrt.f64 (+.f64 (.f64 (+.f64 y a) y) b))) (.f64 y (cbrt.f64 (+.f64 (*.f64 y (+.f64 y a)) b)))) c) y) i))

simplify102.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4937	3099
1	4937	3099

prune135.0ms

Filtered

70 candidates to 82 candidates (-17.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	82	13	95

Merged error: 28.4b

Counts

95 → 13

localize30.0ms

Local error

Found 4 expressions with local error:

28.1b	(cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b)))
28.1b	(cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b)))
28.1b	(cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b)))
29.0b	(/.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184) y) 7925469156333415/34359738368) y) t) (+.f64 (.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b))) (cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b)))) (cbrt.f64 (.f64 y (+.f64 (*.f64 y (+.f64 y a)) b)))) c) y) i))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`times-frac_binary64`
6×	`cbrt-div_binary64` `associate-*r/_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `pow1_binary64`
3×	`associate-/r_binary64` `pow1/3_binary64` `associate-/l_binary64` `cbrt-prod_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 64

Calls

4 calls:

9.0ms	(cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b)))
9.0ms	(cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b)))
9.0ms	(cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b)))
41.0ms	(/.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184) y) 7925469156333415/34359738368) y) t) (+.f64 (.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b))) (cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b)))) (cbrt.f64 (.f64 y (+.f64 (*.f64 y (+.f64 y a)) b)))) c) y) i))

series1.6s

Counts

4 → 12

Calls

4 calls:

165.0ms	(cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b)))
187.0ms	(cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b)))
163.0ms	(cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b)))
1.1s	(/.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184) y) 7925469156333415/34359738368) y) t) (+.f64 (.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b))) (cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b)))) (cbrt.f64 (.f64 y (+.f64 (*.f64 y (+.f64 y a)) b)))) c) y) i))

simplify108.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4859	2904
1	4859	2904

prune128.0ms

Filtered

62 candidates to 76 candidates (-22.6%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	75	14	89

Merged error: 28.4b

Counts

89 → 14

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 y (+.f64 (.f64 y (+.f64 (*.f64 y (+.f64 y a)) b)) c))
0.1b	(.f64 y (+.f64 (.f64 y (+.f64 y a)) b))
0.3b	(/.f64 1 (/.f64 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b)) c)) i) (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 x y) z)) 471841060772561/17179869184)) 7925469156333415/34359738368)) t)))
29.0b	(/.f64 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b)) c)) i) (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 x y) z)) 471841060772561/17179869184)) 7925469156333415/34359738368)) t))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac_binary64`
64×	`add-sqr-sqrt_binary64`
60×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`associate-/r*_binary64` `add-exp-log_binary64`
15×	`add-cbrt-cube_binary64`
11×	`associate-/r/_binary64`
9×	`pow1_binary64`
8×	`flip3-+_binary64` `flip-+_binary64`
6×	`associate-r_binary64` `associate-l_binary64` `associate-/l*_binary64` `div-inv_binary64`
5×	`div-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `rec-exp_binary64` `*-commutative_binary64`
1×	`inv-pow_binary64` `pow-flip_binary64`

Counts

4 → 157

Calls

4 calls:

14.0ms	(.f64 y (+.f64 (.f64 y (+.f64 (*.f64 y (+.f64 y a)) b)) c))
11.0ms	(.f64 y (+.f64 (.f64 y (+.f64 y a)) b))
31.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b)) c)) i) (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 x y) z)) 471841060772561/17179869184)) 7925469156333415/34359738368)) t)))
53.0ms	(/.f64 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b)) c)) i) (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 x y) z)) 471841060772561/17179869184)) 7925469156333415/34359738368)) t))

series2.1s

Counts

4 → 12

Calls

4 calls:

112.0ms	(.f64 y (+.f64 (.f64 y (+.f64 (*.f64 y (+.f64 y a)) b)) c))
54.0ms	(.f64 y (+.f64 (.f64 y (+.f64 y a)) b))
807.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b)) c)) i) (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 x y) z)) 471841060772561/17179869184)) 7925469156333415/34359738368)) t)))
1.1s	(/.f64 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b)) c)) i) (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 x y) z)) 471841060772561/17179869184)) 7925469156333415/34359738368)) t))

simplify121.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4978	9739
1	4978	9739

prune214.0ms

Filtered

117 candidates to 169 candidates (-44.4%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	167	2	169
Fresh	1	10	11
Picked	1	0	1
Done	0	2	2
Total	169	14	183

Merged error: 28.4b

Counts

183 → 14

regimes368.0ms

Accuracy

0% (1.1b remaining)

Error of 29.2b against oracle of 28.1b and baseline of 29.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	79
1	46	79

end0.0ms

sample1.1s

Algorithm

intervals

Results

711.0ms	8000×	body	128	valid
20.0ms	244×	body	128	invalid

Details

analyze2.0s

sample40.0ms

simplify208.0ms

prune4.0ms

localize30.0ms

rewrite81.0ms

series1.0s

simplify80.0ms

prune207.0ms

localize36.0ms

rewrite90.0ms

series1.4s

simplify102.0ms

prune135.0ms

localize30.0ms

rewrite81.0ms

series1.6s

simplify108.0ms

prune128.0ms

localize29.0ms

rewrite140.0ms

series2.1s

simplify121.0ms

prune214.0ms

regimes368.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling